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Simplifying 10x2 + 16x = 16 Reorder the terms: 16x + 10x2 = 16 Solving 16x + 10x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 16x + 10x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 16x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 8x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 8x + 5x2)' equal to zero and attempt to solve: Simplifying -8 + 8x + 5x2 = 0 Solving -8 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 1.6x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 1.6x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 1.6x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 1.6x + x2 = 0 + 1.6 1.6x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 1.6x + x2 = 1.6 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 1.6 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 1.6 + 0.64 Combine like terms: 1.6 + 0.64 = 2.24 0.64 + 1.6x + x2 = 2.24 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (x + 0.8) equal to 1.496662955 and -1.496662955.Subproblem 1
x + 0.8 = 1.496662955 Simplifying x + 0.8 = 1.496662955 Reorder the terms: 0.8 + x = 1.496662955 Solving 0.8 + x = 1.496662955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.496662955 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.496662955 + -0.8 x = 1.496662955 + -0.8 Combine like terms: 1.496662955 + -0.8 = 0.696662955 x = 0.696662955 Simplifying x = 0.696662955Subproblem 2
x + 0.8 = -1.496662955 Simplifying x + 0.8 = -1.496662955 Reorder the terms: 0.8 + x = -1.496662955 Solving 0.8 + x = -1.496662955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.496662955 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.496662955 + -0.8 x = -1.496662955 + -0.8 Combine like terms: -1.496662955 + -0.8 = -2.296662955 x = -2.296662955 Simplifying x = -2.296662955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.696662955, -2.296662955}Solution
x = {0.696662955, -2.296662955}
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